Augmented composite likelihood for copula modeling in family studies under biased sampling

Abstract

SummaryThe heritability of chronic diseases can be effectively studied by examining the nature and extent of within-family associations in disease onset times. Families are typically accrued through a biased sampling scheme in which affected individuals are identified and sampled along with their relatives who may provide right-censored or current status data on their disease onset times. We develop likelihood and composite likelihood methods for modeling the within-family association in these times through copula models in which dependencies are characterized by Kendall's τ . Auxiliary data from independent individuals are exploited by augmentating composite likelihoods to increase precision of marginal parameter estimates and consequently increase efficiency in dependence parameter estimation. An application to a motivating family study in psoriatic arthritis illustrates the method and provides some evidence of excessive paternal transmission of risk.

Testing the heritability and parent‐of‐origin hypotheses for ages at onset of psoriatic arthritis under biased sampling

“…We considered parametric (Weibull and Gamma) and semiparametric (piecewise constant hazard) approaches for the marginal onset time distribution . When the piecewise constant approach is specified, we followed Zhong and Cook () and considered here and in the sequel, four cut points are chosen to be 25, 32, 40, and 48 corresponding to the , , , and quantiles of the right‐truncated onset time of PsA in the clinical cohort. The obtained test statistic , as well as its variance and P value are presented in Table .…”

“…Finally, the UTPAR data contains very little information about the marginal distribution of the ages of onset of PsA as the observations of the probands are right‐truncated and the prevalence of disease among nonprobands is relatively low. To overcome this difficulty, Zhong and Cook () merged the UTPAR data with auxiliary data from a cross‐sectional survey (Gelfand et al ., ) in their analyses. The latter data set includes information on ages at onset of PsA from unrelated individuals.…”

“…Zhong and Cook () fitted their model to UTPAR data merged with survey data and detected significant excessive paternal transmission based on a Wald test. However, their strategy to model the correlation matrix of the Gaussian copula did not exploit the relatedness and shared genetic structure of the family.…”

“…In the present work, motivated by the UTPAR data, we consider the same multivariate survival model as Zhong and Cook () but use an alternative approach to express the correlation matrix of the Gaussian copula. For each pair of related individuals, we follow the spirit of Mott et al .…”

“…Merging the two data sets may improve the efficiency of the estimation of the parameters of the marginal distribution of the disease onset age under the assumption that registry data and the auxiliary data share the same marginal distribution parameters (Pitkäniemi et al, 2009). Zhong and Cook (2016) fitted their model to UTPAR data merged with survey data and detected significant excessive paternal transmission based on a Wald test. However, their strategy to model the correlation matrix of the Gaussian copula did not exploit the relatedness and shared genetic structure of the family.…”